A particle of mass m = 1.18 kg is attached between two identical springs on å frictionless, horizontal tabletop. Both springs have spring constant k and are initially unstressed, and a particle is at x = 0. a) The particle is pulled a distance x along a direction perpendicular to the initial configuration of the springs as shown. Show that the force exerted by the springs on the particle is: Overhead view X-0- L F=-2kx| 1- Vx+L² b) show that the potential energy of the system is U (x)=kx²+ 2kL (L-Vx²+L²) c) Make a plot of U(x) versus x and identify all equilibrium points. Assume L = 1.20 m and k = 40.0 N/ m. wwwww

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A particle of mass m = 1.18 kg is attached between two identical springs on
å frictionless, horizontal tabletop. Both springs have spring constant k and are
initially unstressed, and a particle is at x = 0. a) The particle is pulled a
distance x along a direction perpendicular to the initial configuration of the
springs as shown. Show that the force exerted by the springs on the particle is:
Overhead view
X-0-
L
F=-2kx|1-
Vx+L
b) show that the potential energy of the system is U(x)=kx²+2kL(L-Vx²+L*)
c) Make a plot of U(x) versus x and identify all equilibrium points. Assume L = 1.20 m and k = 40.0 N/
m.
d) If the particle is pulled 0.50 m to the right and released, what is its speed when it reaches x = 0?
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Transcribed Image Text:A particle of mass m = 1.18 kg is attached between two identical springs on å frictionless, horizontal tabletop. Both springs have spring constant k and are initially unstressed, and a particle is at x = 0. a) The particle is pulled a distance x along a direction perpendicular to the initial configuration of the springs as shown. Show that the force exerted by the springs on the particle is: Overhead view X-0- L F=-2kx|1- Vx+L b) show that the potential energy of the system is U(x)=kx²+2kL(L-Vx²+L*) c) Make a plot of U(x) versus x and identify all equilibrium points. Assume L = 1.20 m and k = 40.0 N/ m. d) If the particle is pulled 0.50 m to the right and released, what is its speed when it reaches x = 0? ww wwwwwww
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